Royden'S Compactification of Riemannian Spaces

摘要

Royden's compactification R* of a noncompact Riemannian space R is constructed and properties of HBD- and HD-functions on R are investigated. The tools employed are weak* topology and Riesz representation theorem, all introduced in earlier work of H. Royden and M. Nakai. The results constitute an extension to general Riemannian spaces, of arbitrary dimension n > 2, of properties known for such classes of functions on a Riemann surface. (Author)